The course will begin on monday, October 17,
with two mini-courses on
Reaction-Diffusion Equations for the description of Population Dynamics
Instructors: Dr. Tommaso Lorenzi (St Andrews University, Scotland) - first part
Prof. L. Almeida (CNRS and UPMC Paris) - second part
ABSTRACT AND SYLLABUS
During the last eighty years, reaction-diusion equations have been extensively used to achieve a better
understanding of a wide range of ecological phenomena. The goal of this mini course is to provide
a gentle introduction to reaction-diusion equations arising in the mathematical modelling of population
dynamics. In particular, the cases of space-structured populations and phenotype-structured
populations will be considered. The main qualitative properties of the solutions to these equations
will be studied and examples of possible real world applications will be discussed. The course will be
organised into two related parts as follows:
Part 1. Reaction-diusion equations for space-structured populations
1.1 Local reaction-diusion equations modelling space dispersal
1.2 Local reaction-diusion equations modelling spatial dynamics of invasion
1.3 Local reaction-diusion equations modelling competitive interactions
Part 2. Phenotype-structured models for tumour growth
2.1 Simple models for tumour growth
2.2 Mathematical models for natural selection
2.3 Mathematical models for mutation-selection dynamics
Recommended Books
J.D. Murray
Mathematical Biology I: An Introduction
Springer, 3rd ed. 2003
J.D. Murray
Mathematical Biology II: Spatial Models and Biomedical Applications
Springer, 3rd ed. 2003
B. Perthame
Transport Equations in Biology
Birkhauser, 2007
B. Perthame
Parabolic Equations in Biology - Growth, Reaction, Movement and Diusion
Springer, 2015
